Summary

This project seeks to improve on the Howard et al. (2020) methods used to estimate sport fish harvest, catches and releases of rockfish in Alaska waters. This is essentially a Bayesian version of the Howard methods that allows for more appropriate and defensible sharing of information between areas, handles missing data in a more appropriate manor, accurately propagates uncertainty throughout the estimation procedure and thus does not rely on the decision tree approach in the original Howard methods. Furthermore, the Bayesian approach should provide sport fish harvest, catch and mortality estimates back to 1978 when the SWHS was implemented. Harvest estimates should be mostly consistent with Howard estimates during contemporary times, but may differ based on more appropriate weighting of SWHS and logbook data, including estimating and correcting bias in the SWHS data. Furthermore, the Howard methods are wholly reliant on logbook release estimates and ignore the release estimates from the SWHS data (inferred from the catch and harvest estimates). Here we explore several models that attempt to balance all of the data in estimating releases.

Data

Harvest data was available for 22 commercial fishing management areas in Southcentral and Southeast Alaska. Areas with negligible rockfish harvest were pooled with adjacent areas for analysis. Specifically the Aleutian and Bering areas were pooled into an area labeled BSAI; the IBS and EKYT were pooled into an area labeled EKYKT; the Southeast, Southwest, SAKPEN and Chignik areas were pooled into an area labeled SOKO2PEN and the Westside and Mainland areas were pooled into an area labeled WKMA.

Stateside Harvest Survey (SWHS)

Statewide harvest survey estimates of rockfish catch and harvest are available for 28 years (1996-2023) for all users and for 13 years (2011-2023) for guided anglers (Figure 0). Additionally, there are estimates from 1977- 1995 that required some partitioning work to ascribe to current management units. Harvests in unknown areas were apportioned based on harvest proportions in 1996. Variance estimates are not available for pre-1996 data and as such, the maximum observed coefficient of variation (cv) in each commercial fisheries management unit was applied.

**Figure 0.**- Data sources for estimating rockfish harvests and releases in ADF&G commercial fisheries management units.

Figure 0.- Data sources for estimating rockfish harvests and releases in ADF&G commercial fisheries management units.


SWHS estimates are believed to be biased to some degree. These modelling efforts aim to estimate and correct for that bias with the assumption that logbook harvests are a census of guided harvests.

Rockfish release estimates are inferred from the difference between catch and harvest estimates.

Adam noted that the first 5 years (23 years counting the historical data) in the SWHS data set for PWSO seem unreasonable (close to zero and not corroborated with logbook estimates). Adam recommended setting these harvests to unknown, but current model development has included the data. Once a satisfactory model has been identified we will exam the effects of censoring the PWSO data.

Creel Surveys

NA

Guide Logbooks

Sport fishing guides were required to report their harvest of rockfish for 26 years (1998-2023). Reported harvest is also available by assemblage (pelagic vs. non-pelagic). Harvest of yelloweye and “other” (non-pelagic, non-yelloweye) rockfish were reported separately beginning in 2006.

Logbooks also record the number of rockfish released for the same categories. However, the reliability of the release data is somewhat questionable as reported releases are generally far lower than that estimated by the SWHS. As such several treatments of the data are considered.

Logbook versus SWHS estimates

Estimates of guided harvests and releases from the SWHS do not align with the census from charter logbooks. Logbook harvest reports are generally considered reliable and are used to assess the bias in SWHS reports. However, there is even greater disparity between release estimates in the two sources and it is debatable whether logbook releases should be treated as a census. The Howard et al. (2020) methods do treat the logbook release data as “true” and thus are considerably less than would be estimated from the SWHS data.

**Figure 1.**- SWHS harvest estimates from guided trips (Hhat) versus repoted harvests from charter logbooks (H_lb).

Figure 1.- SWHS harvest estimates from guided trips (Hhat) versus repoted harvests from charter logbooks (H_lb).


The Howard methods treat the logbook release data as a census and then use the ratio of guided:unguided releases in the SWHS to expand the logbook release estimates to generate total and unguided estimates.

To evaluate this discrepancy, several models were used to estimate releases in this exploration. One method (\(LB_{fit}\)) considers the logbook release data to be reliable and a second method (\(LB_{cens}\)) treats the logbook release data as estimates of the minimum released, thus giving more weight to SWHS release estimates. A third method (\(LB_{hyb}\)) is a hybrid approach that treats reported releases of yelloweye as reliable but total rockfish and pelagic rockfish releases as minimums. Model development to date has revealed a tension between the total and pelagic logbook releases and the yelloweye logbook releases.

Composition data

Harvest sampling data exists from Gulf of Alaska areas since 1996 and from Southeast Alaska areas since 2006. Port sampling data is comprised of the number of total rockfish, pelagic and non-pelagic rockfish, black rockfish and yelloweye rockfish.

A current challenge at this juncture is how to accommodate the prohibition on retaining yelloweye in Southeast from 2020 through 2024. Because it is closed to retention the port sampling data is not reflective of releases while remaining an accurate description of the harvest. Current modelling efforts revolve around developing a separate yelloweye curve that censors the missing data.

Process equations

The true harvest \(H_{ay}\) of rockfish for area \(a\) during year \(y\) is assumed to follow a temporal trend defined by a penalized spline:

\[\begin{equation} \textrm{log}(H_{ay})~\sim~\textrm{Normal}(f(a,y), {\sigma_H}) \end{equation}\]

where \(f(a,y)\) in a p-spline basis with 7 components (knots) and a second degree penalty. The variance, \(\sigma_H\), was given a normal prior with a mean and standard deviation of 0.25 and 1, respectively.

Charter and private harvest \(H_{ayu}\) (where u = 1 for charter anglers and u = 2 for private anglers) is a fraction of total annual harvest in each area:

\[\begin{equation} H_{ay1}~=~H_{ay}P_{(user)ay1}\\H_{ay2}~=~H_{ay}(1-P_{(user)ay1}) \end{equation}\]

where \(P_{(user)ay1}\) is the fraction of the annual harvest in each area taken by charter anglers. \(P_{(user)ay1}\) was modeled hierarchically across years as:

\[\begin{equation} P_{(user)ay1}~\sim~\textrm{beta}(\lambda1_a, \lambda2_a) \end{equation}\]

with non-informative priors on both parameters.

Annual black rockfish harvest \(H_{(black)ayu}\) for each area and user group is:

\[\begin{equation} H_{(black)ayu}~=~H_{ayu}P_{(pelagic)ayu}P_{(black|pelagic)ayu} \end{equation}\]

where \(P_{(pelagic)ayu}\) is the fraction of the annual harvest for each area and user group that was pelagic rockfish and \(P_{(black|pelagic)ayu}\) is the fraction of the annual harvest of pelagic rockfish for each area and user group that was black rockfish.

The southeast region also tracks two other non-pelagic rockfish assemblages, demersal shelf rockfish (DSR, which includes yelloweye) and slope rockfish. For the southeast region the harvest of those two assemblages is thus

\[\begin{equation} H_{(DSR)ayu}~=~H_{ayu}(1-P_{(pelagic)ayu})P_{(DSR|non-pelagic)ayu}\\ H_{(slope)ayu}~=~H_{ayu}(1-P_{(pelagic)ayu})P_{(slope|non-pelagic)ayu}\\ \end{equation}\]

where \(P_{(DSR|non-pelagic)ayu}\) and \(P_{(slope|non-pelagic)ayu}\) are the fractions of the annual harvest of non-pelagic rockfish for each area and user group that were DSR and slope rockfish, respectively.

Annual yelloweye rockfish harvest \(H_{(yelloweye)ayu}\) for each area and user group is calculated differently for central/Kodiak areas and southeast areas. For central and Kodiak areas yelloweye rockfish harvests are calculated as

\[\begin{equation} H_{(yelloweye)ayu}~=~H_{ayu}(1-P_{(pelagic)ayu})P_{(yelloweye|non-pelagic)ayu} \end{equation}\]

where \(P_{(yellow|non-pelagic)ayu}\) is the fraction of the annual harvest of non-pelagic rockfish for each area and user group that was yelloweye rockfish.

For southeast areas yelloweye harvests are a fraction of the DSR harvests such that

\[\begin{equation} H_{(yelloweye)ayu}~=~H_{(DSR)ayu}P_{(yelloweye|DSR)ayu} \end{equation}\]

The composition parameters \(P_{(comp)ayu}\), were modeled using a logistic curve that would allow hindcasting without extrapolating beyond the limit of observed values such that:

\[\begin{equation} \textrm{logit}(P_{(comp)ayu})~=~\beta1_{(comp)ayu} + \frac{\beta2_{(comp)ayu}}{(1 + exp(\beta3_{(comp)ayu}*(y - \beta4_{(comp)ayu})))} + \beta5_{(comp)ayu}*I(u=private)+re_{(comp)ayu} \end{equation}\]

where the \(\beta\) parameters define the intercept, scaling factor, slope, inflection point and private angler effect, respectively, \(y\) is the year index, \(I(u=private)\) is an index variable which is 1 when the user groups is private and 0 otherwise and \(re_{(comp)ayu}\) is a random effect with a non-informative prior.

The true number of released rockfish \(R_{ayu}\) were based on the proportion of the total catch harvested by area, year, user group and species grouping , \(pH_{(comp)ayu}\). Thus, converting \(H_{(comp)ayu}\) to total catches by user group, \(C_{(comp)ayu}\), with \(pH_{(comp)ayu}\) results in estimates of total releases such that

\[\begin{equation} R_{(comp)ayu}~=~ C_{(comp)ayu} - H_{(comp)ayu} ~=~ \frac{H_{(comp)ayu}}{pH_{(comp)ayu}} - H_{(comp)ayu} \end{equation}\]

with total releases equal to the sum of the compositional releases.

The proportion harvest parameters for \(pH_{(comp)ayu}\) were modeled using a logistic curve that would allow hindcasting based on trends in the data without extrapolating beyond the range of observed values such that

\[\begin{equation} \textrm{logit}(pH_{(pH)ayuc})~=~\beta1_{(pH)ayu} + \frac{\beta2_{(pH)ayuc}}{(1 + exp(\beta3_{(pH)ayuc}*(y - \beta4_{(pH)ayuc})))} + \beta5_{(pH)ayuc}*I(u=private)+re_{(pH)ayuc} \end{equation}\]

A random effect term allowed estimation during the historical period when data is available, but the curve defined by the above equation determined release estimates between 1977 and 1990.

Observation equations

SWHS estimates of annual rockfish harvest \(\widehat{SWHS}_H{ay}\) were assumed to index true harvest:

\[\begin{equation} \widehat{SWHS}_H{ay}~\sim~\textrm{LogNormal}\left(\textrm{log}(H_{ay}b_{ay}), \sigma_{SWHSHay}^2\right) \end{equation}\]

where bias in the SWHS harvest estimates \(b_H{ay}\) is modeled hierarchically across years as:

\[\begin{equation} b_H{ay}~\sim~\textrm{Normal}(\mu_H{(b)a}, \sigma_H{(b)a}) \end{equation}\]

with non-informative priors on both parameters.

SWHS estimates of guided angler harvest \(\widehat{SWHS}_H{ay1}\) are related to total harvest by:

\[\begin{equation} \widehat{SWHS}_H{ay1}~\sim~\textrm{LogNormal}\left(\textrm{log}(H_{ay1}b_{ay}), \sigma_{SWHS_{ay1}}^2\right) \end{equation}\]

Reported guide logbook harvest \(\widehat{LB}_H{ay}\) is related to true harvest as:

\[\begin{equation} \widehat{LB}_H{ay}~\sim~\textrm{Poisson}(H_{ay1})\\ \widehat{LB}_H{(pelagic)ay}~\sim~\textrm{Poisson}(H_{ay1}P_{(pelagic)ay1})\\ \widehat{LB}_H{(yelloweye)ay}~\sim~\textrm{Poisson}(H_{(yelloweye)ay1})\\ \widehat{LB}_H{(nonpel,nonye)ay}~\sim~\textrm{Poisson}(H_{(nonpel,nonye)ay1})\\ \end{equation}\]

Note that for central and Kodiak areas \(H_{(nonpel,nonye)ay1}\) is equal to the total harvest minus pelagic and yelloweye harvests. For southeast areas \(H_{(nonpel,nonye)ay1}\) is equal to the sum of the DSR and slope harvests minus yelloweye harvests.

SWHS estimates of annual rockfish releases \(\widehat{SWHS}_R{ay}\) were assumed to index true releases in a similar fashion and thus modeled similarly. Because logbook release data is more questionable and demonstrates greater disagreement with SWHS estimates (Figure 1), several approaches have been explored. In the first approach model \(LB_{fit}\) treats the release data as a true census and the releases are related to true releases just as harvests were modeled such that:

\[\begin{equation} \widehat{LB}_R{ay}~\sim~\textrm{Poisson}(R_{ay1})\\ \widehat{LB}_R{(pelagic)ay}~\sim~\textrm{Poisson}(R_{ay1}P_{(pelagic)ay1})\\ \widehat{LB}_R{(yelloweye)ay}~\sim~\textrm{Poisson}(R_{(yelloweye)ay1})\\ \widehat{LB}_R{(nonpel,nonye)ay}~\sim~\textrm{Poisson}(R_{(nonpel,nonye)ay1})\\ \end{equation}\]

Similar to how harvests were modeled, central and Kodiak \(R_{(nonpel,nonye)ay1}\) was equal to total releases minus pelagic and yelloweye releases while for southeast areas it was equal to the sum of DSR and slope releases minues yelloweye releases.

In the second approach we consider the logbook release data to be a minimal estimate of the true releases. Thus model \(LB_{cens}\) censors the release data (censored data is entered as NA) and treats the reported releases as a minimal number such that

\[\begin{equation} \text{censored} \widehat{LB}_R{ay}~\sim~\textrm{LogNormal}\left(\log(R_{ay}), 1\right)\text{T}\left(\widehat{LB}_R{ay}, \infty\right)\\ \text{censored} \widehat{LB}_R{(pelagic)ay}~\sim~\textrm{LogNormal}\left(\log(R_{(pelagic)ay}), 1\right)\text{T}\left(\widehat{LB}_R{(pelagic)ay}, \infty\right)\\ \text{censored} \widehat{LB}_R{(ye)ay}~\sim~\textrm{LogNormal}\left(\log(R_{(ye)ay}), 1\right)\text{T}\left(\widehat{LB}_R{(ye)ay}, \infty\right)\\ \text{censored} \widehat{LB}_R{(nonpel,nonye)ay}~\sim~\textrm{LogNormal}\left(\log(R_{(nonpel,nonye)ay}), 1\right)\text{T}\left(\widehat{LB}_R{(nonpel,nonye)ay}, \infty\right) \end{equation}\]

Model \(LB_{hyb}\) is a hybrid approach that treats the yelloweye releases as a reliable census of yelloweye releases (given the emphasis and ease of recording these fish) but censors the pelagic and total rockfish release estimates such that

\[\begin{equation} \text{censored} \widehat{LB}_R{ay}~\sim~\textrm{LogNormal}\left(\log(R_{ay}), 1\right)\text{T}\left(\widehat{LB}_R{ay}, \infty\right) \\ \text{censored} \widehat{LB}_R{(pelagic)ay}~\sim~\textrm{LogNormal}\left(\log(R_{(pelagic)ay}), 1\right)\text{T}\left(\widehat{LB}_R{(pelagic)ay}, \infty\right) \\ \widehat{LB}_R{(yelloweye)ay}~\sim~\textrm{Poisson}(R_{(yelloweye)ay1})\\ \widehat{LB}_R{(nonpel,nonye)ay}~\sim~\textrm{Poisson}(R_{(nonpel,nonye)ay1})\\ \end{equation}\]

SWHS estimates of guided angler release \(\widehat{SWHS}_R{ay1}\) is modeled the same as harvests.

SWHS release bias was modeled differently in the \(LB_{fit}\), \(LB_{cens}\), and \(LB_{hyb}\) models. Because the \(LB_{fit}\) model assumes that logbook release data is true and the poison likelihoods assume a much smaller variance than the large variances associated with the SWHS release estimates, SWHS release estimates \(b_R{ay}\) were modeled independently of the harvest bias \(b_H{ay}\) such that

\[\begin{equation} b_R{ay}~\sim~\textrm{Normal}(\mu_R{(b)a}, \sigma_R{(b)a}) \end{equation}\]

where bias in the SWHS release estimates \(b_R{ay}\) is modeled hierarchically across years as:

\[\begin{equation} b_R{ay}~\sim~\textrm{Normal}(\mu_R{(b)a}, \sigma_R{(b)a}) \end{equation}\]

with non-informative priors on both parameters.

The \(LB_{cens}\) model treats the logbook release data as lower bound on the release estimates and thus the likelihood linking true releases to the SWHS release estimates is dominant. During model development it was apparent that estimating bias in the SWHS data was more difficult and a different structure was employed that assumed bias in SWHS release data followed a similar pattern to that of the harvests but is offset by some area specific amount. In these models \(b_R{ay}\) differed from \(b_H{ay}\) by offset \(Rboff_{a}\) such that

\[\begin{equation} b_R{ay}~=~b_H{ay} + Rboff_{ay} \end{equation}\]

where

\[\begin{equation} Rboff_{a}~\sim~\textrm{Normal}(\mu_{(bR)r}, \sigma_{(bR)r}) \end{equation}\]

such that \(Rboff_{a}\) was modeled hierarchically across region r.

The number of pelagic rockfish sampled in harvest sampling programs \(x_{(pelagic)ayu}\) follow a binomial distribution:

\[\begin{equation} x_{(pelagic)ayu}~\sim~\textrm{Binomial}(P_{(pelagic)ayu}, N_{ayu}) \end{equation}\]

where \(N_{ayu}\) is the total number of rockfish sampled in area \(a\) during year \(y\) form user group \(u\). The number of black rockfish sampled in harvest sampling programs and the number of yellow rockfish sampled modeled analogously with an appropriately substituted \(N\).

Unresolved issues and outstanding questions:

Models detailed in this markdown represent the next step in the modelling process whereby the pH parameters are separated out by species. This approach separates the compositional data that is germaine to the harvests from the release estimates and releases are now based on pH. Additionally, this approach allows the pH parameters to differ between pelagic and yelloweye which is appropriate given regulatory changes as well as fisherman and industry behaviour and is born out in the results. The approach results in great uncertainty around unguided release estimates, but that uncertainty is appropriate given the data. These models handle the yelloweye closures in southeast much more appropriately given that the compositional data is no longer directly applied to the release estimates. These versions of the model are in development and it is unclear whether the \(LB_{cens}\) model would work, but it appears applicable to the \(LB_{fit}\) and \(LB_{hyb}\) approaches.

Other issues include:

  1. Complete convergence has not been achieved and the logistic curve parameters for p_pelagic and p_yellow remain the last sticking point. I think that p_pelagic will resolve with longer chains.
  2. Estimate precision: These models are producing more precise harvest estimates that in Adam’s original model. I am not sure why at this juncture. sigma_H on the spline was switched from a fixed value to a prior centered around that fixed value, but the model estimates are in the same range as the fixed value. Would the number of knots in the spline explain this? 7 knots was settled on during early model fitting when it clearly performed better than fewer or more knots.
  3. Prior choices in general need to be vetted. The priors on the logistic curves are fairly informed in an effort to achieve the desired shapes for hindcasting. Ideally, sensitivity testing would occur but the model is very slow to converge. The beta parameters on the logistic curves have required a lot of work on the priors to reach convergence.
  4. Random effects on pH: These are currently used in the model but because pH isn’t linked to data as the p_comp data is I am not sure what to make of them or if they are appropriate.
  5. Model comparisons: I need to write code for comparing models side by side as well as quantifying the differences between these methods and the Howard methods.

Results

**Figure X.**- Rhat values and proportion of parameters that converged (Rhat < 1.1.)

Figure X.- Rhat values and proportion of parameters that converged (Rhat < 1.1.)

Estimate comparison

Since previous estimates of rockfish harvest have been produced these first 3 graphs will be used to show how the modeled estimates compare to the estimates produced earlier. For total rockfish the estimates are in general agreement although differences are noted. These estimates should be more reliable because they include both SWHS and guide logbook data, handle variance more appropriately, use hierarchical distributions when data is missing, directly consider observation error and are produced using reproducible research.

**Figure 2.**- Total rockfish harvests 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 2.- Total rockfish harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 3.**- Total rockfish releases 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 3.- Total rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.


Notes from Adam: When looking at only black rockfish the most significant differences are for the Prince William Sound Inside area. I did not spend a great deal of time tracking this down although it looks like the previous version used bad values for \(P_{(black)ayu}\) for at least unguided anglers. For the moment I would ignore the results for BSIA and SOKO2SAP. I think it is possible to give approximate values for these areas but it will require a little more coding which I have yet to do.

**Figure 4.**- Black rockfish harvests 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 4.- Black rockfish harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.


And black rockfish releases…

**Figure 5.**- Black rockfish releases 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 5.- Black rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 6.**- Yellow rockfish harvests 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 6.- Yellow rockfish harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 7.**- Yellow rockfish releases 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 7.- Yellow rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 6.**- DSR rockfish harvests 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 6.- DSR rockfish harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 7.**- DSR rockfish releases 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 7.- DSR rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 6.**- Slope rockfish harvests 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 6.- Slope rockfish harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 7.**- Slope rockfish releases 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 7.- Slope rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Model fit

Logbook residuals

**Figure 8.**- Residuals from logbook harvests

Figure 8.- Residuals from logbook harvests


SWHS residuals

**Figure 9.**- Residuals from SWHS harvests.

Figure 9.- Residuals from SWHS harvests.



**Figure 10.**- Residual of SWHS releases

Figure 10.- Residual of SWHS releases

Parameter estimates

P(Charter)

These histograms show the posterior distribution of the mean percent of rockfish harvested by the charter fleet.

**Figure 11.**- Mean percent of harvest by charter anglers.

Figure 11.- Mean percent of harvest by charter anglers.


When considered annually we see the percent of rockfish harvested by the charter fleet follows our data fairly well although we just do not have much information about this ratio. Prior to 2011 the percent charter is confounded with SWHS bias and should be mostly discounted.

**Figure 12.**- Annual estimates of the percent of harvest by charter anglers for 16 commerical fishing manamgent areas, 1996-2023.

Figure 12.- Annual estimates of the percent of harvest by charter anglers for 16 commerical fishing manamgent areas, 1996-2023.

P(Harvest)

These plots show the fitted logistic line to the proportion of caught rockfish that are harvested. These estimates are used for hindcasting catch estimates based on the harvest data in early years when catch estimates are unavailable.


**Figure 13.**- Annual proportion of pelagic rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available.

Figure 13.- Annual proportion of pelagic rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available.


**Figure 13.**- Annual proportion of yelloweye rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available.

Figure 13.- Annual proportion of yelloweye rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available.


**Figure 13.**- Annual proportion of non-pelagic, non-yelloweye rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available. Note, that this is not estimated for Southeast areas because non=pelagics are divided between DSR (including yelloweye) and Slope species.

Figure 13.- Annual proportion of non-pelagic, non-yelloweye rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available. Note, that this is not estimated for Southeast areas because non=pelagics are divided between DSR (including yelloweye) and Slope species.


## NULL


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SWHS bias

Figure 14 shows the mean estimate for SWHS bias. Cook Inlet, North Gulf Coast and North Southeast Inside all look pretty good while most other areas have substantial bias. Prince William Sound Inside has the largest bias.

**Figure 14.**- Mean SWHS bias for harvests and catches. Note that a bias < 1 indicates that the SWHS *underestimates* the true value and bias > 1 indicates the survey *overestimates* the true value.

Figure 14.- Mean SWHS bias for harvests and catches. Note that a bias < 1 indicates that the SWHS underestimates the true value and bias > 1 indicates the survey overestimates the true value.


Our estimates of SWHS bias track observations fairly well when he have guided harvest estimates. There are some disturbing trends/patterns seen in the earlier time periods. Often the patterns represent periods where SWHS estimates and guide logbook estimates do not follow the recent relationship. I’m not sure what drives the trends but it seems plausible to me that long-term changes in the ratio of charter and private anglers may be a factor. If Charter/Private ratio information is available in the historical creel data it my be helpful here (particularly for North Southeast Inside and South Southeast outside).

**Figure 15.**- Annual estimates of SWHS bias in harvests and releases for 16 commerical fishing manamgent areas, 1996-2023. Note that a bias < 1 indicates that the SWHS *underestimates* the true value and bias > 1 indicates the survey *overestimates* the true value.

Figure 15.- Annual estimates of SWHS bias in harvests and releases for 16 commerical fishing manamgent areas, 1996-2023. Note that a bias < 1 indicates that the SWHS underestimates the true value and bias > 1 indicates the survey overestimates the true value.

P(pelagic)

We model the percentage of pelagic rockfish in the harvest because we have the information for charter anglers (via logbooks) starting in 1998. Other than looking at the model estimates you can use Figure 8 to compare the two data streams for pelagic rockfish harvest. In general they are in agreement with major exceptions in Price William Sound inside, Prince William Sound outside (early in the time series) and South Southeast inside.

**Figure 16.**- Annual estimates of the percent of the sport harvest that was pelagic rockfish for 16 commerical fishing manamgent areas, 1996-2023.

Figure 16.- Annual estimates of the percent of the sport harvest that was pelagic rockfish for 16 commerical fishing manamgent areas, 1996-2023.

P(black|pelagic)

Note that in Southeast Alaska we only have composition data starting in 2006. Tania dug up old SE data, but it did not provide any useful data for species apportionment.

**Figure 17.**- Annual estimates of the percent of the sport harvest of pelagic rockfish that were black rockfish for 16 commerical fishing manamgent areas, 1996-2023.

Figure 17.- Annual estimates of the percent of the sport harvest of pelagic rockfish that were black rockfish for 16 commerical fishing manamgent areas, 1996-2023.

P(yelloweye|non-pelagic / yelloweye|DSR)

**Figure 18.**- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were yelloweye rockfish for 16 commerical fishing manamgent areas, 1996-2023. Note that P(yelloweye) is the the proportion relative to non-pelagics for Central and Kodiak areas but is relative to DSR for Southeast areas.

Figure 18.- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were yelloweye rockfish for 16 commerical fishing manamgent areas, 1996-2023. Note that P(yelloweye) is the the proportion relative to non-pelagics for Central and Kodiak areas but is relative to DSR for Southeast areas.

P(DSR|non-pelagic)

**Figure 18.**- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were DSR rockfish for 6 Southeast commerical fishing manamgent areas, 1996-2023.

Figure 18.- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were DSR rockfish for 6 Southeast commerical fishing manamgent areas, 1996-2023.

P(slope|non-pelagic)

**Figure 18.**- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were slope rockfish for 6 southeast commerical fishing manamgent areas, 1996-2023. Note that P(yelloweye) is the the proportion relative to non-pelagics for Central and Kodiak areas but is relative to DSR for Southeast areas.

Figure 18.- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were slope rockfish for 6 southeast commerical fishing manamgent areas, 1996-2023. Note that P(yelloweye) is the the proportion relative to non-pelagics for Central and Kodiak areas but is relative to DSR for Southeast areas.



Summary of unconverged parameters:

Table 1. Summary of unconverged parameters including the number (n) and the average Rhat from the unconverged parameters.
parameter n badRhat_avg
beta1_black 1 4.659131
beta0_black 1 3.790476
beta3_black 1 1.909800
beta3_pelagic 1 1.514454
beta2_black 1 1.464193
sd_comp 1 1.336706
beta2_pelagic 5 1.294334
beta3_pH 1 1.245733
beta1_yellow 2 1.216068
parameter n badRhat_avg
beta4_pelagic 3 1.200470
beta2_pH 1 1.192042
beta0_pH 1 1.183966
beta1_pelagic 5 1.177374
beta1_pH 8 1.176177
tau_beta0_pH 1 1.150696
beta2_yellow 1 1.149176
beta0_pelagic 1 1.122115
Table 2. Summary of unconverged parameters by area
afognak BSAI CI CSEO eastside EWYKT NG northeast NSEI NSEO PWSI PWSO SOKO2SAP SSEI SSEO WKMA
beta0_black 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0
beta0_pelagic 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0
beta0_pH 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
beta1_black 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0
beta1_pelagic 1 1 0 1 0 0 1 0 0 0 0 0 0 0 0 1
beta1_pH 0 1 1 0 1 0 0 1 0 0 1 1 1 0 0 1
beta1_yellow 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1
beta2_black 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0
beta2_pelagic 0 0 0 1 1 1 0 0 0 0 0 0 0 1 1 0
beta2_pH 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
beta2_yellow 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0
beta3_black 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0
beta3_pelagic 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0
beta3_pH 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
beta4_pelagic 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 1
sd_comp 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
tau_beta0_pH 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0

Parameter estimates:

Summary Table of Parameter Estimates
Parameter mean sd Lower_CI Median Upper_CI
mu_bc_H[1] -0.132 0.072 -0.269 -0.137 0.024
mu_bc_H[2] -0.095 0.045 -0.176 -0.098 0.003
mu_bc_H[3] -0.432 0.069 -0.571 -0.432 -0.291
mu_bc_H[4] -0.992 0.192 -1.374 -0.989 -0.624
mu_bc_H[5] 0.946 1.002 -0.133 0.755 3.196
mu_bc_H[6] -2.166 0.333 -2.838 -2.168 -1.494
mu_bc_H[7] -0.467 0.112 -0.696 -0.467 -0.256
mu_bc_H[8] 0.231 0.363 -0.360 0.201 0.988
mu_bc_H[9] -0.293 0.134 -0.556 -0.295 -0.036
mu_bc_H[10] -0.113 0.070 -0.246 -0.117 0.033
mu_bc_H[11] -0.124 0.038 -0.199 -0.124 -0.051
mu_bc_H[12] -0.251 0.106 -0.474 -0.246 -0.050
mu_bc_H[13] -0.136 0.078 -0.284 -0.138 0.023
mu_bc_H[14] -0.305 0.096 -0.493 -0.302 -0.125
mu_bc_H[15] -0.345 0.050 -0.441 -0.346 -0.242
mu_bc_H[16] -0.257 0.394 -0.928 -0.283 0.607
mu_bc_R[1] 1.301 0.142 1.032 1.299 1.585
mu_bc_R[2] 1.449 0.096 1.251 1.451 1.634
mu_bc_R[3] 1.378 0.137 1.104 1.381 1.638
mu_bc_R[4] 0.920 0.196 0.498 0.925 1.276
mu_bc_R[5] 1.153 0.477 0.235 1.161 2.096
mu_bc_R[6] -1.583 0.438 -2.453 -1.576 -0.727
mu_bc_R[7] 0.329 0.193 -0.062 0.332 0.699
mu_bc_R[8] 0.558 0.203 0.153 0.562 0.933
mu_bc_R[9] 0.328 0.212 -0.132 0.349 0.697
mu_bc_R[10] 1.325 0.126 1.063 1.332 1.558
mu_bc_R[11] 1.036 0.099 0.843 1.038 1.226
mu_bc_R[12] 0.827 0.208 0.404 0.831 1.224
mu_bc_R[13] 1.023 0.102 0.823 1.025 1.223
mu_bc_R[14] 0.899 0.140 0.621 0.904 1.160
mu_bc_R[15] 0.783 0.111 0.563 0.783 1.000
mu_bc_R[16] 1.093 0.129 0.827 1.095 1.347
tau_pH[1] 5.279 0.455 4.427 5.273 6.219
tau_pH[2] 2.463 0.300 1.924 2.443 3.085
tau_pH[3] 2.225 0.217 1.810 2.218 2.662
beta0_pH[1,1] 0.501 0.178 0.144 0.506 0.837
beta0_pH[2,1] 1.327 0.189 0.940 1.336 1.675
beta0_pH[3,1] 1.420 0.190 1.018 1.434 1.754
beta0_pH[4,1] 1.566 0.219 1.083 1.585 1.940
beta0_pH[5,1] -0.851 0.280 -1.454 -0.838 -0.336
beta0_pH[6,1] -0.635 0.467 -1.775 -0.556 0.026
beta0_pH[7,1] 0.369 0.623 -0.955 0.725 0.967
beta0_pH[8,1] -0.664 0.291 -1.342 -0.627 -0.196
beta0_pH[9,1] -0.643 0.290 -1.256 -0.625 -0.141
beta0_pH[10,1] 0.210 0.191 -0.171 0.211 0.577
beta0_pH[11,1] -0.121 0.175 -0.482 -0.117 0.216
beta0_pH[12,1] 0.477 0.187 0.113 0.483 0.837
beta0_pH[13,1] -0.002 0.147 -0.289 -0.004 0.280
beta0_pH[14,1] -0.322 0.168 -0.664 -0.319 -0.008
beta0_pH[15,1] -0.037 0.176 -0.386 -0.034 0.301
beta0_pH[16,1] -0.482 0.343 -1.323 -0.432 0.034
beta0_pH[1,2] 2.697 0.213 2.200 2.719 3.041
beta0_pH[2,2] 2.786 0.215 2.152 2.813 3.112
beta0_pH[3,2] 2.467 0.293 1.884 2.473 3.087
beta0_pH[4,2] 2.635 0.311 1.950 2.719 3.072
beta0_pH[5,2] 4.467 1.404 2.547 4.200 7.936
beta0_pH[6,2] 2.831 0.284 2.290 2.833 3.366
beta0_pH[7,2] 1.899 0.201 1.462 1.916 2.241
beta0_pH[8,2] 2.819 0.214 2.418 2.833 3.165
beta0_pH[9,2] 2.790 0.603 1.614 2.806 3.717
beta0_pH[10,2] 3.679 0.227 3.143 3.693 4.082
beta0_pH[11,2] -4.840 0.286 -5.410 -4.840 -4.282
beta0_pH[12,2] -4.812 0.412 -5.647 -4.796 -4.082
beta0_pH[13,2] -4.597 0.385 -5.374 -4.596 -3.839
beta0_pH[14,2] -5.638 0.468 -6.599 -5.620 -4.797
beta0_pH[15,2] -4.244 0.327 -4.875 -4.241 -3.602
beta0_pH[16,2] -4.858 0.390 -5.660 -4.854 -4.117
beta0_pH[1,3] 0.650 0.578 -0.735 0.807 1.399
beta0_pH[2,3] 1.910 0.467 0.561 2.052 2.449
beta0_pH[3,3] 2.311 0.366 1.256 2.392 2.729
beta0_pH[4,3] 2.695 0.507 1.160 2.837 3.218
beta0_pH[5,3] 1.200 1.848 -1.710 0.955 5.852
beta0_pH[6,3] -0.726 1.054 -2.930 -0.818 1.355
beta0_pH[7,3] -2.210 0.673 -3.700 -2.125 -1.204
beta0_pH[8,3] 0.265 0.197 -0.132 0.262 0.652
beta0_pH[9,3] -0.957 0.713 -2.670 -0.719 -0.063
beta0_pH[10,3] -0.166 1.046 -2.446 0.231 1.128
beta0_pH[11,3] -0.155 0.319 -0.776 -0.164 0.497
beta0_pH[12,3] -0.854 0.345 -1.575 -0.835 -0.249
beta0_pH[13,3] -0.133 0.309 -0.760 -0.133 0.460
beta0_pH[14,3] -0.274 0.260 -0.774 -0.278 0.226
beta0_pH[15,3] -0.701 0.302 -1.317 -0.685 -0.146
beta0_pH[16,3] -0.395 0.286 -0.993 -0.394 0.183
beta1_pH[1,1] 3.143 0.323 2.574 3.123 3.829
beta1_pH[2,1] 2.209 0.301 1.691 2.181 2.841
beta1_pH[3,1] 2.013 0.302 1.508 1.987 2.680
beta1_pH[4,1] 2.400 0.349 1.839 2.355 3.243
beta1_pH[5,1] 2.278 0.348 1.691 2.244 3.064
beta1_pH[6,1] 3.839 1.084 2.352 3.622 6.413
beta1_pH[7,1] 2.862 1.997 0.462 2.479 9.267
beta1_pH[8,1] 3.975 0.978 2.645 3.752 6.390
beta1_pH[9,1] 2.324 0.387 1.681 2.288 3.144
beta1_pH[10,1] 2.417 0.270 1.919 2.401 2.979
beta1_pH[11,1] 3.302 0.219 2.889 3.296 3.737
beta1_pH[12,1] 2.562 0.218 2.143 2.558 2.986
beta1_pH[13,1] 2.976 0.217 2.565 2.970 3.412
beta1_pH[14,1] 3.426 0.219 3.012 3.423 3.883
beta1_pH[15,1] 2.542 0.225 2.119 2.539 2.982
beta1_pH[16,1] 4.106 0.638 3.197 3.991 5.584
beta1_pH[1,2] 15.127 37.452 0.000 1.014 142.728
beta1_pH[2,2] 2.605 5.195 0.000 0.846 20.446
beta1_pH[3,2] 1.113 0.373 0.000 1.134 1.752
beta1_pH[4,2] 3.861 8.974 0.000 0.922 32.364
beta1_pH[5,2] 5.297 19.073 0.000 0.937 48.802
beta1_pH[6,2] 1.432 3.825 0.000 1.175 3.547
beta1_pH[7,2] 1.404 2.903 0.000 0.547 9.618
beta1_pH[8,2] 1.540 3.908 0.000 0.493 11.703
beta1_pH[9,2] 1.254 2.521 0.000 1.080 4.245
beta1_pH[10,2] 7.200 17.784 0.000 1.950 69.261
beta1_pH[11,2] 6.679 0.317 6.081 6.677 7.320
beta1_pH[12,2] 6.517 0.494 5.660 6.483 7.527
beta1_pH[13,2] 7.009 0.425 6.189 7.005 7.848
beta1_pH[14,2] 7.294 0.491 6.414 7.269 8.322
beta1_pH[15,2] 6.737 0.356 6.044 6.737 7.443
beta1_pH[16,2] 7.482 0.422 6.689 7.484 8.350
beta1_pH[1,3] 2.818 1.120 1.552 2.492 5.820
beta1_pH[2,3] 0.625 1.327 0.000 0.209 3.422
beta1_pH[3,3] 0.482 1.331 0.000 0.087 3.282
beta1_pH[4,3] 0.524 1.209 0.000 0.102 3.041
beta1_pH[5,3] 3.951 5.087 1.625 3.163 9.928
beta1_pH[6,3] 2.716 1.166 1.134 2.588 4.839
beta1_pH[7,3] 3.055 0.688 2.041 2.949 4.640
beta1_pH[8,3] 2.827 0.374 2.164 2.805 3.600
beta1_pH[9,3] 3.022 0.727 2.057 2.827 4.777
beta1_pH[10,3] 3.578 1.115 2.185 3.184 6.068
beta1_pH[11,3] 2.746 0.369 2.019 2.748 3.488
beta1_pH[12,3] 4.102 0.431 3.293 4.095 5.011
beta1_pH[13,3] 1.717 0.328 1.075 1.713 2.376
beta1_pH[14,3] 2.517 0.341 1.873 2.514 3.213
beta1_pH[15,3] 1.980 0.325 1.374 1.972 2.642
beta1_pH[16,3] 1.800 0.315 1.193 1.800 2.416
beta2_pH[1,1] 0.464 0.116 0.286 0.447 0.732
beta2_pH[2,1] 0.542 0.244 0.238 0.501 1.121
beta2_pH[3,1] 0.611 0.374 0.223 0.532 1.620
beta2_pH[4,1] 0.468 0.184 0.205 0.439 0.900
beta2_pH[5,1] 1.734 1.313 0.254 1.508 5.042
beta2_pH[6,1] 0.188 0.065 0.092 0.178 0.348
beta2_pH[7,1] -1.180 1.872 -6.092 -0.791 1.133
beta2_pH[8,1] 0.248 0.092 0.124 0.231 0.468
beta2_pH[9,1] 0.442 0.243 0.181 0.393 0.986
beta2_pH[10,1] 0.633 0.327 0.300 0.560 1.403
beta2_pH[11,1] 0.768 0.205 0.468 0.739 1.288
beta2_pH[12,1] 1.342 0.517 0.725 1.242 2.565
beta2_pH[13,1] 0.742 0.221 0.414 0.710 1.300
beta2_pH[14,1] 0.833 0.210 0.525 0.802 1.314
beta2_pH[15,1] 0.794 0.331 0.408 0.738 1.504
beta2_pH[16,1] 0.380 0.168 0.172 0.336 0.824
beta2_pH[1,2] -7.126 7.393 -22.044 -6.423 5.486
beta2_pH[2,2] -7.640 6.958 -22.740 -6.762 4.572
beta2_pH[3,2] -8.160 6.179 -22.422 -6.905 -0.732
beta2_pH[4,2] -8.019 6.395 -22.911 -6.691 -0.202
beta2_pH[5,2] -7.639 8.399 -24.473 -7.607 10.518
beta2_pH[6,2] -7.835 8.126 -23.920 -7.708 10.991
beta2_pH[7,2] -7.969 8.177 -24.089 -7.834 10.850
beta2_pH[8,2] -7.839 8.142 -23.820 -7.845 10.442
beta2_pH[9,2] -7.929 8.122 -24.230 -7.863 10.752
beta2_pH[10,2] -8.245 7.983 -23.737 -8.209 10.592
beta2_pH[11,2] -8.796 3.881 -18.720 -7.838 -4.005
beta2_pH[12,2] -6.120 4.440 -16.633 -5.313 -0.754
beta2_pH[13,2] -6.071 4.098 -16.509 -4.958 -1.560
beta2_pH[14,2] -7.235 3.991 -16.895 -6.247 -2.289
beta2_pH[15,2] -8.410 3.734 -17.587 -7.546 -3.571
beta2_pH[16,2] -8.798 3.840 -18.487 -7.963 -3.822
beta2_pH[1,3] 4.304 5.699 0.141 1.316 19.511
beta2_pH[2,3] 4.006 6.509 -7.033 2.406 19.948
beta2_pH[3,3] 3.614 6.740 -6.953 2.061 19.903
beta2_pH[4,3] 3.702 6.586 -7.152 2.191 19.893
beta2_pH[5,3] 6.714 5.897 0.058 5.334 20.743
beta2_pH[6,3] 6.826 6.029 0.106 5.414 21.437
beta2_pH[7,3] 6.562 5.911 0.509 4.623 21.429
beta2_pH[8,3] 7.874 5.496 0.779 6.739 21.858
beta2_pH[9,3] 6.251 6.130 0.298 4.691 21.272
beta2_pH[10,3] 5.462 6.327 0.313 2.105 21.022
beta2_pH[11,3] -2.160 1.722 -7.196 -1.671 -0.616
beta2_pH[12,3] -2.345 1.708 -7.416 -1.854 -0.984
beta2_pH[13,3] -2.734 2.086 -8.908 -2.069 -0.752
beta2_pH[14,3] -2.694 2.004 -8.761 -2.089 -0.893
beta2_pH[15,3] -2.805 2.012 -8.685 -2.180 -0.986
beta2_pH[16,3] -2.860 2.193 -9.370 -2.151 -0.894
beta3_pH[1,1] 35.819 0.809 34.308 35.796 37.492
beta3_pH[2,1] 33.438 1.199 31.390 33.334 36.147
beta3_pH[3,1] 33.814 1.097 31.731 33.790 36.181
beta3_pH[4,1] 33.844 1.216 31.649 33.783 36.431
beta3_pH[5,1] 27.766 1.122 26.531 27.487 31.008
beta3_pH[6,1] 38.900 3.077 33.054 38.807 45.061
beta3_pH[7,1] 25.868 8.770 18.338 21.083 45.418
beta3_pH[8,1] 39.874 2.073 36.250 39.661 44.720
beta3_pH[9,1] 30.684 1.481 28.050 30.570 33.948
beta3_pH[10,1] 32.628 0.883 30.939 32.611 34.430
beta3_pH[11,1] 30.253 0.469 29.334 30.263 31.167
beta3_pH[12,1] 30.163 0.394 29.379 30.169 30.914
beta3_pH[13,1] 33.158 0.574 32.079 33.141 34.344
beta3_pH[14,1] 32.015 0.463 31.153 31.997 32.965
beta3_pH[15,1] 31.172 0.634 29.946 31.182 32.425
beta3_pH[16,1] 32.019 1.008 30.393 31.924 34.314
beta3_pH[1,2] 28.212 7.945 18.354 26.663 43.964
beta3_pH[2,2] 25.310 6.983 18.273 22.371 43.522
beta3_pH[3,2] 41.365 2.900 32.487 41.850 43.774
beta3_pH[4,2] 32.440 8.427 19.269 30.027 44.428
beta3_pH[5,2] 30.958 8.161 18.524 30.453 45.162
beta3_pH[6,2] 33.780 5.357 19.444 35.385 43.160
beta3_pH[7,2] 28.404 7.310 18.474 26.819 44.479
beta3_pH[8,2] 27.954 7.257 18.343 26.499 44.113
beta3_pH[9,2] 37.931 9.136 19.109 43.568 45.760
beta3_pH[10,2] 29.792 5.200 19.179 29.985 41.853
beta3_pH[11,2] 43.396 0.167 43.122 43.380 43.751
beta3_pH[12,2] 43.175 0.188 42.827 43.149 43.616
beta3_pH[13,2] 43.852 0.146 43.492 43.890 44.047
beta3_pH[14,2] 43.287 0.178 43.056 43.247 43.732
beta3_pH[15,2] 43.400 0.181 43.114 43.380 43.796
beta3_pH[16,2] 43.495 0.178 43.172 43.489 43.836
beta3_pH[1,3] 38.854 2.107 34.185 39.509 42.300
beta3_pH[2,3] 31.104 7.362 18.708 31.578 44.605
beta3_pH[3,3] 29.763 8.062 18.329 29.493 44.368
beta3_pH[4,3] 28.798 7.657 18.381 27.592 44.523
beta3_pH[5,3] 26.705 6.700 18.344 25.108 42.595
beta3_pH[6,3] 27.300 6.299 18.706 25.775 44.035
beta3_pH[7,3] 26.520 0.967 24.804 26.399 28.811
beta3_pH[8,3] 41.507 0.341 40.973 41.503 42.071
beta3_pH[9,3] 32.542 1.855 27.234 33.335 34.213
beta3_pH[10,3] 34.826 1.590 31.585 35.479 36.812
beta3_pH[11,3] 41.770 0.820 40.178 41.804 43.230
beta3_pH[12,3] 41.730 0.382 40.989 41.736 42.490
beta3_pH[13,3] 42.723 0.891 41.040 42.731 44.653
beta3_pH[14,3] 41.097 0.561 39.921 41.117 42.128
beta3_pH[15,3] 42.591 0.654 41.162 42.672 43.672
beta3_pH[16,3] 42.881 0.716 41.259 42.980 44.085
beta0_pelagic[1] 1.910 0.469 0.592 2.076 2.422
beta0_pelagic[2] 1.365 0.282 0.569 1.434 1.723
beta0_pelagic[3] 0.177 0.490 -1.328 0.271 0.810
beta0_pelagic[4] 0.171 0.627 -1.746 0.295 1.023
beta0_pelagic[5] 1.057 0.579 -0.691 1.142 1.514
beta0_pelagic[6] 1.437 0.201 0.929 1.457 1.727
beta0_pelagic[7] 1.598 0.136 1.323 1.596 1.864
beta0_pelagic[8] 1.737 0.133 1.480 1.737 1.989
beta0_pelagic[9] 2.528 0.421 1.284 2.646 2.971
beta0_pelagic[10] 2.554 0.136 2.296 2.557 2.814
beta0_pelagic[11] -0.118 0.449 -1.066 -0.086 0.600
beta0_pelagic[12] 1.674 0.140 1.393 1.675 1.945
beta0_pelagic[13] 0.308 0.189 -0.103 0.320 0.647
beta0_pelagic[14] -0.125 0.281 -0.752 -0.095 0.349
beta0_pelagic[15] -0.284 0.138 -0.562 -0.282 -0.011
beta0_pelagic[16] 0.231 0.328 -0.645 0.315 0.642
beta1_pelagic[1] 0.334 0.475 0.000 0.089 1.661
beta1_pelagic[2] 0.233 0.828 0.000 0.069 1.013
beta1_pelagic[3] 0.894 0.643 0.001 0.753 3.054
beta1_pelagic[4] 1.009 0.658 0.000 0.898 2.908
beta1_pelagic[5] 0.105 0.600 0.000 0.000 2.138
beta1_pelagic[6] 0.052 0.228 0.000 0.000 0.819
beta1_pelagic[7] 0.018 0.175 0.000 0.000 0.079
beta1_pelagic[8] 0.010 0.087 0.000 0.000 0.055
beta1_pelagic[9] 0.224 0.522 0.000 0.000 1.767
beta1_pelagic[10] 0.011 0.104 0.000 0.000 0.070
beta1_pelagic[11] 4.034 1.035 2.409 3.915 6.230
beta1_pelagic[12] 2.835 0.310 2.230 2.833 3.449
beta1_pelagic[13] 2.924 0.738 1.792 2.820 4.696
beta1_pelagic[14] 4.426 0.992 2.896 4.297 6.624
beta1_pelagic[15] 2.937 0.268 2.428 2.936 3.482
beta1_pelagic[16] 3.826 1.108 2.703 3.398 6.934
beta2_pelagic[1] 2.052 3.134 -4.516 1.696 8.771
beta2_pelagic[2] 2.083 3.059 -3.965 1.670 9.189
beta2_pelagic[3] 2.336 2.646 0.064 1.526 9.019
beta2_pelagic[4] 2.506 2.639 0.068 1.771 9.030
beta2_pelagic[5] -0.023 2.945 -6.510 0.051 6.414
beta2_pelagic[6] 0.135 2.801 -5.899 0.154 6.015
beta2_pelagic[7] 0.002 2.851 -6.414 0.079 5.974
beta2_pelagic[8] -0.017 2.932 -6.367 0.072 6.334
beta2_pelagic[9] 0.895 2.657 -3.959 0.508 7.909
beta2_pelagic[10] 0.024 2.903 -6.355 0.074 6.302
beta2_pelagic[11] 0.519 1.205 0.109 0.212 4.316
beta2_pelagic[12] 4.038 2.423 0.995 3.492 10.289
beta2_pelagic[13] 0.732 0.932 0.200 0.472 3.189
beta2_pelagic[14] 0.311 0.150 0.159 0.280 0.652
beta2_pelagic[15] 3.793 2.582 1.138 3.187 10.222
beta2_pelagic[16] 2.732 2.766 0.169 1.692 9.344
beta3_pelagic[1] 27.076 7.465 18.469 24.227 44.599
beta3_pelagic[2] 28.338 8.015 18.327 25.903 45.005
beta3_pelagic[3] 29.556 4.755 20.577 29.557 41.923
beta3_pelagic[4] 25.564 3.704 19.855 25.394 36.664
beta3_pelagic[5] 30.545 8.387 18.519 29.303 45.807
beta3_pelagic[6] 30.197 7.785 18.520 29.465 44.727
beta3_pelagic[7] 30.222 8.149 18.496 29.249 45.134
beta3_pelagic[8] 30.069 7.854 18.475 29.327 44.801
beta3_pelagic[9] 30.115 7.544 18.594 29.323 44.839
beta3_pelagic[10] 29.842 7.869 18.502 28.636 44.784
beta3_pelagic[11] 41.906 2.185 37.200 42.294 45.573
beta3_pelagic[12] 43.463 0.278 42.970 43.448 44.005
beta3_pelagic[13] 42.778 1.317 40.268 42.709 45.541
beta3_pelagic[14] 42.413 1.677 38.878 42.506 45.502
beta3_pelagic[15] 43.070 0.314 42.351 43.126 43.572
beta3_pelagic[16] 43.122 0.912 41.117 43.192 45.289
mu_beta0_pelagic[1] 0.849 0.854 -1.041 0.896 2.458
mu_beta0_pelagic[2] 1.797 0.420 0.857 1.807 2.570
mu_beta0_pelagic[3] 0.276 0.477 -0.748 0.297 1.117
tau_beta0_pelagic[1] 1.423 3.766 0.062 0.624 6.944
tau_beta0_pelagic[2] 2.291 2.324 0.182 1.809 7.141
tau_beta0_pelagic[3] 1.524 1.188 0.170 1.219 4.570
beta0_yellow[1] -0.538 0.184 -0.933 -0.525 -0.231
beta0_yellow[2] 0.501 0.173 0.163 0.510 0.799
beta0_yellow[3] -0.289 0.174 -0.629 -0.290 0.049
beta0_yellow[4] 0.811 0.323 -0.103 0.878 1.209
beta0_yellow[5] -1.250 0.403 -2.051 -1.244 -0.481
beta0_yellow[6] 0.283 0.213 -0.137 0.282 0.694
beta0_yellow[7] 1.046 0.183 0.737 1.052 1.349
beta0_yellow[8] 0.652 0.727 -1.408 0.924 1.271
beta0_yellow[9] -0.146 0.331 -0.781 -0.126 0.422
beta0_yellow[10] 0.236 0.154 -0.068 0.236 0.542
beta0_yellow[11] -1.946 0.446 -2.845 -1.935 -1.089
beta0_yellow[12] -3.672 0.432 -4.598 -3.647 -2.894
beta0_yellow[13] -3.774 0.476 -4.761 -3.740 -2.917
beta0_yellow[14] -1.894 0.799 -3.025 -2.076 -0.029
beta0_yellow[15] -2.881 0.442 -3.834 -2.872 -2.053
beta0_yellow[16] -2.431 0.443 -3.299 -2.422 -1.569
beta1_yellow[1] 0.462 0.601 0.000 0.296 1.779
beta1_yellow[2] 1.065 0.376 0.566 1.023 1.836
beta1_yellow[3] 0.617 0.267 0.020 0.625 1.080
beta1_yellow[4] 1.447 0.851 0.624 1.201 4.175
beta1_yellow[5] 2.964 1.044 1.552 2.857 4.901
beta1_yellow[6] 2.268 0.360 1.588 2.261 2.985
beta1_yellow[7] 6.326 9.881 1.470 3.821 23.623
beta1_yellow[8] 2.061 1.901 0.024 1.804 6.033
beta1_yellow[9] 1.667 0.517 0.843 1.624 2.963
beta1_yellow[10] 2.355 0.467 1.490 2.332 3.316
beta1_yellow[11] 2.097 0.443 1.249 2.086 2.995
beta1_yellow[12] 2.481 0.445 1.676 2.443 3.445
beta1_yellow[13] 2.887 0.477 2.044 2.852 3.913
beta1_yellow[14] 2.225 0.869 0.827 2.202 3.331
beta1_yellow[15] 2.120 0.443 1.272 2.106 3.073
beta1_yellow[16] 2.179 0.444 1.331 2.175 3.075
beta2_yellow[1] -3.215 3.146 -10.232 -2.898 2.786
beta2_yellow[2] -3.793 2.610 -9.446 -3.328 -0.210
beta2_yellow[3] -3.489 2.518 -9.537 -3.082 -0.220
beta2_yellow[4] -2.739 2.646 -9.047 -2.006 -0.080
beta2_yellow[5] -4.530 2.888 -11.566 -3.995 -0.623
beta2_yellow[6] 3.540 2.212 0.950 2.941 9.154
beta2_yellow[7] -4.873 2.922 -11.931 -4.334 -0.932
beta2_yellow[8] -2.037 4.190 -10.526 -1.905 6.946
beta2_yellow[9] 3.586 2.593 0.169 3.140 9.661
beta2_yellow[10] -4.505 2.731 -10.937 -4.012 -0.752
beta2_yellow[11] -4.014 2.066 -9.037 -3.528 -1.204
beta2_yellow[12] -4.134 2.005 -9.262 -3.746 -1.415
beta2_yellow[13] -4.119 2.000 -9.224 -3.656 -1.549
beta2_yellow[14] -4.037 2.117 -9.192 -3.694 -0.860
beta2_yellow[15] -3.774 2.012 -8.950 -3.312 -1.126
beta2_yellow[16] -4.140 1.974 -9.113 -3.762 -1.447
beta3_yellow[1] 27.430 7.543 18.339 24.607 44.256
beta3_yellow[2] 29.069 1.744 25.905 28.857 32.729
beta3_yellow[3] 32.928 3.274 23.851 32.937 39.759
beta3_yellow[4] 28.967 3.558 21.186 28.032 36.047
beta3_yellow[5] 33.423 1.232 31.129 33.440 35.561
beta3_yellow[6] 39.690 0.567 38.694 39.642 40.983
beta3_yellow[7] 20.090 1.519 18.561 20.040 21.252
beta3_yellow[8] 24.807 5.697 18.235 23.751 42.342
beta3_yellow[9] 37.805 2.236 35.312 37.617 43.692
beta3_yellow[10] 29.320 0.618 27.816 29.408 30.152
beta3_yellow[11] 45.310 0.513 44.084 45.398 45.973
beta3_yellow[12] 43.318 0.401 42.567 43.293 44.135
beta3_yellow[13] 44.863 0.370 44.044 44.923 45.483
beta3_yellow[14] 42.578 4.610 28.973 44.156 45.812
beta3_yellow[15] 45.192 0.525 44.140 45.187 45.969
beta3_yellow[16] 44.592 0.632 43.426 44.587 45.828
mu_beta0_yellow[1] 0.099 0.568 -1.099 0.098 1.274
mu_beta0_yellow[2] 0.113 0.493 -0.941 0.128 1.092
mu_beta0_yellow[3] -2.398 0.681 -3.455 -2.505 -0.730
tau_beta0_yellow[1] 1.831 2.310 0.098 1.196 7.455
tau_beta0_yellow[2] 1.228 1.128 0.137 0.942 3.988
tau_beta0_yellow[3] 1.373 2.010 0.085 0.822 5.676
beta0_black[1] -0.092 0.155 -0.391 -0.094 0.222
beta0_black[2] 1.910 0.126 1.670 1.910 2.161
beta0_black[3] 1.315 0.133 1.062 1.312 1.579
beta0_black[4] 2.426 0.129 2.172 2.428 2.679
beta0_black[5] 1.607 1.977 -2.748 1.642 5.875
beta0_black[6] 1.557 1.944 -2.853 1.642 5.607
beta0_black[7] 1.650 1.959 -2.555 1.684 5.910
beta0_black[8] 1.288 0.217 0.856 1.288 1.700
beta0_black[9] 2.442 0.240 1.979 2.446 2.910
beta0_black[10] 1.470 0.132 1.213 1.473 1.719
beta0_black[11] 3.487 0.149 3.196 3.490 3.768
beta0_black[12] 4.853 0.169 4.525 4.854 5.186
beta0_black[13] 0.214 0.524 -0.546 0.047 1.096
beta0_black[14] 2.855 0.160 2.547 2.854 3.166
beta0_black[15] 1.294 0.154 0.994 1.293 1.604
beta0_black[16] 4.274 0.154 3.975 4.275 4.570
beta2_black[1] 3.253 2.150 0.648 2.762 8.481
beta2_black[2] 0.000 0.000 0.000 0.000 0.000
beta2_black[3] 0.000 0.000 0.000 0.000 0.000
beta2_black[4] 0.000 0.000 0.000 0.000 0.000
beta2_black[5] 0.000 0.000 0.000 0.000 0.000
beta2_black[6] 0.000 0.000 0.000 0.000 0.000
beta2_black[7] 0.000 0.000 0.000 0.000 0.000
beta2_black[8] 0.000 0.000 0.000 0.000 0.000
beta2_black[9] 0.000 0.000 0.000 0.000 0.000
beta2_black[10] 0.000 0.000 0.000 0.000 0.000
beta2_black[11] 0.000 0.000 0.000 0.000 0.000
beta2_black[12] 0.000 0.000 0.000 0.000 0.000
beta2_black[13] -1.416 3.040 -7.878 -1.320 5.732
beta2_black[14] 0.000 0.000 0.000 0.000 0.000
beta2_black[15] 0.000 0.000 0.000 0.000 0.000
beta2_black[16] 0.000 0.000 0.000 0.000 0.000
beta3_black[1] 41.690 1.670 39.872 41.918 43.140
beta3_black[2] 25.000 0.000 25.000 25.000 25.000
beta3_black[3] 25.000 0.000 25.000 25.000 25.000
beta3_black[4] 25.000 0.000 25.000 25.000 25.000
beta3_black[5] 25.000 0.000 25.000 25.000 25.000
beta3_black[6] 25.000 0.000 25.000 25.000 25.000
beta3_black[7] 25.000 0.000 25.000 25.000 25.000
beta3_black[8] 25.000 0.000 25.000 25.000 25.000
beta3_black[9] 25.000 0.000 25.000 25.000 25.000
beta3_black[10] 25.000 0.000 25.000 25.000 25.000
beta3_black[11] 25.000 0.000 25.000 25.000 25.000
beta3_black[12] 25.000 0.000 25.000 25.000 25.000
beta3_black[13] 36.518 6.015 19.887 39.106 42.835
beta3_black[14] 25.000 0.000 25.000 25.000 25.000
beta3_black[15] 25.000 0.000 25.000 25.000 25.000
beta3_black[16] 25.000 0.000 25.000 25.000 25.000
beta4_black[1] -0.255 0.191 -0.622 -0.252 0.116
beta4_black[2] 0.246 0.179 -0.095 0.245 0.605
beta4_black[3] -0.932 0.190 -1.300 -0.934 -0.569
beta4_black[4] 0.417 0.210 0.002 0.418 0.837
beta4_black[5] 0.205 2.730 -4.453 0.113 5.548
beta4_black[6] 0.208 2.535 -4.527 0.137 4.961
beta4_black[7] 0.186 2.764 -4.517 0.121 4.923
beta4_black[8] -0.697 0.362 -1.394 -0.696 0.004
beta4_black[9] 1.466 1.025 -0.099 1.313 3.864
beta4_black[10] 0.024 0.185 -0.329 0.022 0.386
beta4_black[11] -0.696 0.209 -1.090 -0.696 -0.296
beta4_black[12] 0.168 0.327 -0.455 0.166 0.837
beta4_black[13] -1.178 0.217 -1.594 -1.178 -0.761
beta4_black[14] -0.187 0.232 -0.635 -0.193 0.266
beta4_black[15] -0.886 0.213 -1.312 -0.884 -0.482
beta4_black[16] -0.603 0.225 -1.042 -0.601 -0.165
mu_beta0_black[1] 1.256 0.928 -0.732 1.304 3.102
mu_beta0_black[2] 1.601 0.882 -0.479 1.644 3.298
mu_beta0_black[3] 2.602 0.939 0.524 2.653 4.375
tau_beta0_black[1] 0.597 0.552 0.054 0.432 2.020
tau_beta0_black[2] 1.981 4.076 0.054 0.838 10.145
tau_beta0_black[3] 0.269 0.189 0.051 0.220 0.772
beta0_dsr[11] -2.885 0.286 -3.433 -2.879 -2.324
beta0_dsr[12] 4.530 0.276 3.993 4.528 5.080
beta0_dsr[13] -1.348 0.314 -1.921 -1.337 -0.774
beta0_dsr[14] -3.717 0.527 -4.806 -3.706 -2.727
beta0_dsr[15] -1.936 0.280 -2.486 -1.935 -1.399
beta0_dsr[16] -2.996 0.354 -3.680 -2.988 -2.319
beta1_dsr[11] 4.824 0.299 4.240 4.813 5.425
beta1_dsr[12] 6.643 8.956 2.358 5.099 19.737
beta1_dsr[13] 2.858 0.353 2.284 2.840 3.485
beta1_dsr[14] 6.385 0.554 5.345 6.381 7.495
beta1_dsr[15] 3.339 0.284 2.773 3.342 3.906
beta1_dsr[16] 5.817 0.374 5.067 5.816 6.559
beta2_dsr[11] -8.299 2.376 -13.857 -7.919 -4.736
beta2_dsr[12] -7.094 2.699 -13.267 -6.837 -2.346
beta2_dsr[13] -6.426 2.778 -12.449 -6.241 -1.472
beta2_dsr[14] -6.137 2.672 -12.193 -5.930 -1.903
beta2_dsr[15] -7.808 2.435 -13.629 -7.447 -4.050
beta2_dsr[16] -7.947 2.333 -13.669 -7.563 -4.344
beta3_dsr[11] 43.492 0.150 43.224 43.488 43.777
beta3_dsr[12] 33.977 0.741 32.050 34.137 34.817
beta3_dsr[13] 43.234 0.335 42.807 43.184 43.855
beta3_dsr[14] 43.338 0.229 43.072 43.277 43.893
beta3_dsr[15] 43.510 0.184 43.175 43.509 43.852
beta3_dsr[16] 43.446 0.159 43.173 43.438 43.768
beta4_dsr[11] 0.579 0.208 0.172 0.581 0.987
beta4_dsr[12] 0.258 0.430 -0.589 0.252 1.118
beta4_dsr[13] -0.161 0.213 -0.585 -0.157 0.245
beta4_dsr[14] 0.155 0.247 -0.311 0.159 0.637
beta4_dsr[15] 0.721 0.212 0.312 0.719 1.132
beta4_dsr[16] 0.144 0.230 -0.309 0.145 0.598
beta0_slope[11] -1.933 0.164 -2.255 -1.932 -1.622
beta0_slope[12] -4.675 0.268 -5.227 -4.671 -4.167
beta0_slope[13] -1.340 0.204 -1.802 -1.324 -0.992
beta0_slope[14] -2.643 0.183 -3.006 -2.640 -2.282
beta0_slope[15] -1.368 0.164 -1.689 -1.365 -1.046
beta0_slope[16] -2.713 0.176 -3.054 -2.714 -2.381
beta1_slope[11] 4.596 0.305 4.007 4.588 5.202
beta1_slope[12] 5.000 0.520 4.035 4.995 6.044
beta1_slope[13] 2.922 0.523 2.228 2.855 4.423
beta1_slope[14] 6.529 0.565 5.461 6.521 7.667
beta1_slope[15] 3.051 0.292 2.477 3.049 3.609
beta1_slope[16] 5.372 0.397 4.588 5.376 6.161
beta2_slope[11] 8.071 2.372 4.419 7.708 13.761
beta2_slope[12] 7.187 2.525 2.747 7.005 12.909
beta2_slope[13] 5.721 2.919 0.415 5.781 11.688
beta2_slope[14] 6.530 2.449 2.482 6.325 12.086
beta2_slope[15] 7.528 2.393 3.544 7.229 13.167
beta2_slope[16] 7.640 2.356 3.867 7.347 13.169
beta3_slope[11] 43.471 0.150 43.199 43.469 43.765
beta3_slope[12] 43.412 0.237 43.062 43.382 43.890
beta3_slope[13] 43.639 0.423 42.938 43.702 44.257
beta3_slope[14] 43.316 0.173 43.091 43.274 43.772
beta3_slope[15] 43.517 0.198 43.156 43.523 43.870
beta3_slope[16] 43.459 0.167 43.179 43.448 43.791
beta4_slope[11] -0.575 0.224 -1.020 -0.579 -0.148
beta4_slope[12] -1.393 0.660 -2.856 -1.326 -0.349
beta4_slope[13] 0.051 0.222 -0.372 0.042 0.501
beta4_slope[14] -0.177 0.257 -0.679 -0.183 0.331
beta4_slope[15] -0.722 0.214 -1.150 -0.721 -0.307
beta4_slope[16] -0.207 0.236 -0.660 -0.214 0.271
sigma_H[1] 0.195 0.053 0.099 0.192 0.308
sigma_H[2] 0.172 0.030 0.119 0.170 0.237
sigma_H[3] 0.196 0.043 0.116 0.194 0.290
sigma_H[4] 0.415 0.077 0.285 0.407 0.593
sigma_H[5] 0.995 0.209 0.617 0.984 1.455
sigma_H[6] 0.400 0.200 0.038 0.395 0.813
sigma_H[7] 0.295 0.059 0.204 0.287 0.430
sigma_H[8] 0.414 0.088 0.265 0.406 0.605
sigma_H[9] 0.526 0.124 0.334 0.510 0.807
sigma_H[10] 0.216 0.042 0.143 0.213 0.309
sigma_H[11] 0.279 0.046 0.201 0.274 0.382
sigma_H[12] 0.440 0.166 0.208 0.423 0.773
sigma_H[13] 0.215 0.037 0.152 0.212 0.296
sigma_H[14] 0.508 0.094 0.343 0.500 0.707
sigma_H[15] 0.248 0.040 0.178 0.243 0.337
sigma_H[16] 0.224 0.042 0.152 0.220 0.318
lambda_H[1] 3.015 3.864 0.166 1.724 13.132
lambda_H[2] 7.982 7.435 0.722 5.819 28.070
lambda_H[3] 6.358 9.946 0.293 3.013 31.976
lambda_H[4] 0.006 0.004 0.001 0.005 0.018
lambda_H[5] 4.100 9.586 0.036 1.068 29.862
lambda_H[6] 7.816 15.551 0.009 1.137 52.242
lambda_H[7] 0.015 0.011 0.002 0.012 0.042
lambda_H[8] 8.237 9.915 0.062 4.799 35.186
lambda_H[9] 0.015 0.010 0.003 0.013 0.040
lambda_H[10] 0.314 0.654 0.037 0.206 1.136
lambda_H[11] 0.278 0.458 0.011 0.135 1.260
lambda_H[12] 5.015 7.103 0.184 2.700 24.370
lambda_H[13] 3.493 3.313 0.289 2.511 12.636
lambda_H[14] 3.535 4.654 0.218 2.080 15.145
lambda_H[15] 0.027 0.047 0.003 0.017 0.107
lambda_H[16] 0.810 1.071 0.045 0.423 3.911
mu_lambda_H[1] 4.370 1.931 1.221 4.152 8.503
mu_lambda_H[2] 3.864 1.981 0.563 3.675 8.089
mu_lambda_H[3] 3.492 1.812 0.778 3.257 7.700
sigma_lambda_H[1] 8.651 4.318 1.982 8.098 18.243
sigma_lambda_H[2] 8.384 4.719 1.021 7.772 18.448
sigma_lambda_H[3] 6.309 4.012 0.987 5.483 16.627
beta_H[1,1] 6.903 1.093 4.288 7.070 8.563
beta_H[2,1] 9.880 0.491 8.796 9.905 10.771
beta_H[3,1] 7.992 0.760 6.189 8.084 9.264
beta_H[4,1] 9.541 7.724 -6.642 9.847 24.527
beta_H[5,1] 0.083 2.259 -4.885 0.234 3.994
beta_H[6,1] 3.205 3.924 -6.836 4.635 7.568
beta_H[7,1] 1.337 5.584 -10.818 1.613 11.399
beta_H[8,1] 1.530 4.489 -2.294 1.256 3.672
beta_H[9,1] 13.273 5.658 1.877 13.283 24.499
beta_H[10,1] 7.104 1.723 3.603 7.197 10.307
beta_H[11,1] 5.232 3.517 -2.679 6.083 10.075
beta_H[12,1] 2.622 1.099 0.803 2.556 4.950
beta_H[13,1] 9.041 0.909 7.101 9.124 10.498
beta_H[14,1] 2.194 1.053 0.147 2.199 4.353
beta_H[15,1] -6.019 3.902 -12.976 -6.178 2.356
beta_H[16,1] 3.464 2.656 -0.785 3.128 9.562
beta_H[1,2] 7.913 0.242 7.411 7.920 8.376
beta_H[2,2] 10.024 0.135 9.760 10.027 10.279
beta_H[3,2] 8.948 0.197 8.556 8.946 9.344
beta_H[4,2] 3.516 1.479 0.709 3.469 6.637
beta_H[5,2] 1.957 0.940 0.067 1.971 3.720
beta_H[6,2] 5.775 1.045 3.323 5.937 7.397
beta_H[7,2] 2.402 1.094 0.433 2.339 4.762
beta_H[8,2] 2.978 1.228 1.223 3.143 4.240
beta_H[9,2] 3.485 1.107 1.322 3.444 5.787
beta_H[10,2] 8.199 0.344 7.484 8.218 8.814
beta_H[11,2] 9.753 0.638 8.822 9.609 11.189
beta_H[12,2] 3.946 0.370 3.258 3.925 4.713
beta_H[13,2] 9.125 0.251 8.671 9.115 9.638
beta_H[14,2] 4.026 0.355 3.352 4.017 4.732
beta_H[15,2] 11.339 0.699 9.862 11.357 12.616
beta_H[16,2] 4.548 0.801 2.984 4.564 6.071
beta_H[1,3] 8.478 0.233 8.059 8.465 8.949
beta_H[2,3] 10.069 0.116 9.841 10.068 10.306
beta_H[3,3] 9.618 0.164 9.306 9.616 9.966
beta_H[4,3] -2.458 0.890 -4.270 -2.457 -0.714
beta_H[5,3] 3.822 0.613 2.568 3.830 4.936
beta_H[6,3] 7.981 1.168 6.363 7.623 10.503
beta_H[7,3] -2.483 0.755 -3.953 -2.481 -1.036
beta_H[8,3] 5.280 0.561 4.672 5.200 6.343
beta_H[9,3] -2.864 0.742 -4.378 -2.850 -1.440
beta_H[10,3] 8.699 0.271 8.167 8.699 9.233
beta_H[11,3] 8.541 0.289 7.907 8.559 9.063
beta_H[12,3] 5.250 0.316 4.523 5.291 5.767
beta_H[13,3] 8.839 0.179 8.479 8.842 9.184
beta_H[14,3] 5.723 0.277 5.118 5.739 6.210
beta_H[15,3] 10.382 0.325 9.742 10.380 11.030
beta_H[16,3] 6.254 0.601 4.965 6.299 7.311
beta_H[1,4] 8.271 0.175 7.878 8.282 8.584
beta_H[2,4] 10.125 0.121 9.882 10.129 10.348
beta_H[3,4] 10.117 0.161 9.759 10.132 10.400
beta_H[4,4] 11.798 0.442 10.928 11.794 12.669
beta_H[5,4] 5.458 0.720 4.265 5.376 7.011
beta_H[6,4] 7.069 0.931 4.913 7.336 8.326
beta_H[7,4] 8.150 0.352 7.438 8.154 8.820
beta_H[8,4] 6.708 0.267 6.172 6.726 7.134
beta_H[9,4] 7.190 0.468 6.271 7.191 8.136
beta_H[10,4] 7.770 0.232 7.334 7.763 8.245
beta_H[11,4] 9.391 0.200 8.992 9.397 9.777
beta_H[12,4] 7.137 0.219 6.714 7.136 7.587
beta_H[13,4] 9.041 0.144 8.748 9.046 9.312
beta_H[14,4] 7.729 0.215 7.322 7.723 8.168
beta_H[15,4] 9.460 0.237 9.002 9.463 9.913
beta_H[16,4] 9.343 0.240 8.917 9.323 9.845
beta_H[1,5] 8.978 0.145 8.688 8.985 9.255
beta_H[2,5] 10.784 0.093 10.604 10.782 10.970
beta_H[3,5] 10.921 0.177 10.605 10.912 11.297
beta_H[4,5] 8.391 0.456 7.518 8.381 9.289
beta_H[5,5] 5.418 0.586 4.093 5.473 6.460
beta_H[6,5] 8.801 0.623 7.898 8.656 10.306
beta_H[7,5] 6.836 0.336 6.209 6.828 7.529
beta_H[8,5] 8.219 0.225 7.850 8.203 8.704
beta_H[9,5] 8.222 0.473 7.290 8.218 9.185
beta_H[10,5] 10.075 0.224 9.639 10.073 10.515
beta_H[11,5] 11.503 0.231 11.065 11.509 11.957
beta_H[12,5] 8.485 0.201 8.094 8.484 8.884
beta_H[13,5] 10.013 0.130 9.761 10.012 10.268
beta_H[14,5] 9.196 0.229 8.781 9.181 9.666
beta_H[15,5] 11.164 0.246 10.685 11.167 11.651
beta_H[16,5] 9.918 0.180 9.552 9.925 10.256
beta_H[1,6] 10.182 0.188 9.864 10.165 10.596
beta_H[2,6] 11.514 0.107 11.306 11.514 11.721
beta_H[3,6] 10.806 0.169 10.432 10.819 11.092
beta_H[4,6] 12.865 0.812 11.257 12.877 14.435
beta_H[5,6] 5.874 0.602 4.756 5.877 7.055
beta_H[6,6] 8.774 0.675 6.943 8.899 9.772
beta_H[7,6] 9.767 0.541 8.723 9.767 10.855
beta_H[8,6] 9.515 0.302 8.924 9.538 9.966
beta_H[9,6] 8.454 0.788 6.917 8.451 10.047
beta_H[10,6] 9.520 0.313 8.836 9.545 10.075
beta_H[11,6] 10.820 0.347 10.076 10.842 11.429
beta_H[12,6] 9.371 0.256 8.859 9.363 9.895
beta_H[13,6] 11.049 0.160 10.770 11.036 11.388
beta_H[14,6] 9.828 0.294 9.244 9.829 10.407
beta_H[15,6] 10.843 0.433 9.972 10.844 11.705
beta_H[16,6] 10.537 0.239 10.032 10.550 10.969
beta_H[1,7] 10.883 0.867 8.806 11.002 12.309
beta_H[2,7] 12.221 0.445 11.287 12.229 13.093
beta_H[3,7] 10.557 0.663 9.064 10.621 11.696
beta_H[4,7] 2.541 4.088 -5.272 2.493 10.465
beta_H[5,7] 6.452 1.896 3.110 6.383 10.512
beta_H[6,7] 9.646 2.350 5.118 9.580 15.685
beta_H[7,7] 10.877 2.713 5.442 10.846 16.157
beta_H[8,7] 11.000 1.131 9.387 10.922 13.045
beta_H[9,7] 4.491 4.037 -3.471 4.498 12.511
beta_H[10,7] 9.822 1.450 7.188 9.702 13.042
beta_H[11,7] 10.992 1.694 7.785 10.873 14.705
beta_H[12,7] 10.024 0.914 8.123 10.106 11.565
beta_H[13,7] 11.662 0.718 9.993 11.730 12.809
beta_H[14,7] 10.399 0.942 8.392 10.468 12.038
beta_H[15,7] 11.989 2.238 7.716 11.946 16.591
beta_H[16,7] 12.296 1.246 10.182 12.168 15.067
beta0_H[1] 8.481 12.764 -18.977 8.809 33.735
beta0_H[2] 10.753 6.571 -2.062 10.762 24.121
beta0_H[3] 9.808 9.699 -11.312 9.972 29.389
beta0_H[4] 15.428 181.149 -363.154 15.474 385.252
beta0_H[5] 3.977 25.500 -44.178 4.035 47.989
beta0_H[6] 8.736 47.860 -99.251 7.822 124.209
beta0_H[7] 6.297 125.141 -240.371 10.014 256.775
beta0_H[8] 6.990 35.959 -16.393 6.593 30.796
beta0_H[9] 5.818 120.373 -231.184 6.919 255.603
beta0_H[10] 8.938 32.673 -56.013 9.034 76.254
beta0_H[11] 9.802 48.509 -92.838 9.167 112.970
beta0_H[12] 6.655 12.165 -15.058 6.709 29.899
beta0_H[13] 9.952 13.006 -10.586 9.883 30.648
beta0_H[14] 7.236 11.716 -15.629 7.192 32.853
beta0_H[15] 9.312 106.007 -205.127 10.272 234.121
beta0_H[16] 8.420 25.682 -44.671 7.803 59.854